The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1  1  1 12  1  1 10  0  6  1  1 10  1  1  1 12  1  6  1  1  0  1  6  1  6  1  1  1 12  1  1  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5 10 15  1 12  9  1  1  1  0  3  1  5 15  6  1 15  1 12  9  1  0  1 12  1 10  5  6  1  9  9  5  3  5  0
 0  0  8  0  0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  0  8  0  0  0  8  0  8  0  8  0  8  8  8  8  0  0  0  8  0  8  8  0  0  8  0  0  8  0  0
 0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  0  0  8  0  0  8  0  8  8  0  8  8  8  8  0  0  0  8  0  8  0  0  8  8  8  8  8  0  0  0  0  0  8  0  8  8  0
 0  0  0  0  8  0  0  0  0  8  8  0  0  8  8  8  0  8  8  8  0  0  8  0  0  0  8  0  0  0  8  0  8  8  8  8  0  0  0  0  8  0  8  0  8  8  0  0  8  0  8  0
 0  0  0  0  0  8  0  0  8  8  0  0  0  0  8  0  0  8  8  8  8  8  8  8  8  8  8  0  8  0  8  0  8  0  0  0  0  0  8  0  0  8  8  8  8  0  0  8  8  8  8  0
 0  0  0  0  0  0  8  0  8  0  0  8  8  0  8  0  8  0  8  0  0  0  0  8  8  0  0  8  8  0  8  8  0  8  0  0  8  8  8  8  8  8  0  8  0  8  8  0  0  8  0  0
 0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  0  8  8  0  0  0  8  8  0  8  0  0  0  8  8  8  0  0  8  8  0  8  8  0  0  8  0  0  0  8  8  0  8  8  8  0

generates a code of length 52 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+40x^44+66x^45+118x^46+366x^47+788x^48+1002x^49+2312x^50+1894x^51+3253x^52+1894x^53+2303x^54+1002x^55+757x^56+366x^57+104x^58+66x^59+18x^60+12x^62+5x^64+8x^66+1x^68+7x^70+1x^72

The gray image is a code over GF(2) with n=416, k=14 and d=176.
This code was found by Heurico 1.16 in 2.68 seconds.